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{-# LANGUAGE TemplateHaskell, RankNTypes, TypeOperators, DataKinds,
PolyKinds, TypeFamilies, GADTs #-}
module RAE_T32a where
import Data.Kind
data family Sing (k :: Type) :: k -> Type
data TyArr' (a :: Type) (b :: Type) :: Type
type TyArr (a :: Type) (b :: Type) = TyArr' a b -> Type
type family (a :: TyArr k1 k2) @@ (b :: k1) :: k2
data TyPi' (a :: Type) (b :: TyArr a Type) :: Type
type TyPi (a :: Type) (b :: TyArr a Type) = TyPi' a b -> Type
type family (a :: TyPi k1 k2) @@@ (b :: k1) :: k2 @@ b
$(return [])
data MkStar (p :: Type) (x :: TyArr' p Type)
type instance MkStar p @@ x = Type
$(return [])
data Sigma (p :: Type) (r :: TyPi p (MkStar p)) :: Type where
Sigma ::
forall (p :: Type) (r :: TyPi p (MkStar p)) (a :: p) (b :: r @@@ a).
Sing Type p -> Sing (TyPi p (MkStar p)) r -> Sing p a ->
Sing (r @@@ a) b -> Sigma p r
$(return [])
data instance Sing Sigma (Sigma p r) x where
SSigma ::
forall (p :: Type) (r :: TyPi p (MkStar p)) (a :: p) (b :: r @@@ a)
(sp :: Sing Type p) (sr :: Sing (TyPi p (MkStar p)) r)
(sa :: Sing p a) (sb :: Sing (r @@@ a) b).
Sing (Sing (r @@@ a) b) sb ->
Sing (Sigma p r) ('Sigma sp sr sa sb)
-- I (RAE) believe this last definition is ill-typed.
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